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Bifurcations and chaos of the Bonhoeffer-van der Pol model. (English) Zbl 0677.92009
Summary: Periodic and chaotic behaviour of the Bonhoeffer-van der Pol model of a nerve membrane driven by a periodic stimulating current $a\sb 1 \cos \omega t$ is investigated. Results show that there exist ordinary and reversed period-doubling cascades and a mode-locking state. At low driving amplitudes $a\sb 1$, there are period-doubling and chaotic states, but no impulse solutions. When $a\sb 1$ is larger than $a\sb 0=0.749$, there are chaotic, reversed period-doubling, and mode-locking states and there also exist impulse trains. A mode-locking state with period 4 over a very large range of amplitudes is also found. At $a\sb 1=1.7059$ the system goes back to a one-period state.

92CxxPhysiological, cellular and medical topics
34C05Location of integral curves, singular points, limit cycles (ODE)
34C25Periodic solutions of ODE
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